Faster-Than-Nyquist (FTN) is a signaling technique in which a sequence of pulse-shaped symbols is transmitted at a symbol rate that is higher than the Nyquist rate defined for the pulse shape being used. FTN was originally presented by Mazo in “Faster-Than-Nyquist Signaling,” Bell Systems Technical Journal, volume 54, October, 1975, pages 1451-1462, which is incorporated herein by reference.
Several communication techniques that use FTN have been described. For example, Liveris and Georghiades describe FTN techniques that use raised-cosine pulses in “Exploiting Faster-Than-Nyquist Signaling,” IEEE Transactions on Communications, volume 51, September, 2003, pages 1502-1511, which is incorporated herein by reference. Rusek and Anderson describe FTN techniques that use non-binary signal constellations and precoding filters, in “Non Binary and Precoded Faster Than Nyquist Signaling,” IEEE Transactions on Communication, volume 56, number 5, May, 2008, pages 808-817, which is incorporated herein by reference.
Communication systems sometimes use transmitter precoding schemes in order to mitigate impairments such as Inter-Symbol Interference (ISI). An example precoding technique, known as the Tomlinson-Harashima Precoding (THP), is described by Tomlinson in “New Automatic Equalizer Employing Modulo Arithmetic,” IEEE Electronic Letters, volume 7, number 5, March, 1971, pages 138-139, which is incorporated herein by reference. Wesel and Cioffi present maximum bounds on the achievable information rates of several THP schemes in “Achievable Rates for Tomlinson-Harashima Precoding,” IEEE Transactions on Information Theory, volume 44, number 2, March, 1998, pages 824-831, which is incorporated herein by reference. Another precoding scheme, referred to as Laroia-Tretter-Farvardin precoding, is described by Laroia et al., in “A Simple and Effective Precoding Scheme for Noise Whitening on Intersymbol Interference Channels,” IEEE Transactions on Communication, volume 41, number 10, October, 1993, pages 1460-1463, which is incorporated herein by reference.
Other precoding schemes involve lattice coding. Interference cancellation using lattice coding is described, for example, by Erez et al., in “Capacity and Lattice Strategies for Cancelling Known Interference,” IEEE Transactions on Information Theory, volume 51, number 11, November, 2005, pages 3820-3833, which is incorporated herein by reference. Other lattice coding techniques are proposed by Zamir et al., in “Nested Linear/Lattice Codes for Structured Multiterminal Binning,” IEEE Transactions on Information Theory, volume 48, number 6, June, 2002, pages 1250-1276, which is incorporated herein by reference.